Related papers: Boundary singularities of N -harmonic functions

In this paper, we study the approximation of negative plurifinely plurisubharmonic function defined on a plurifinely domain by an increasing sequence of plurisubharmonic functions defined in Euclidean domains.

A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…

We prove that, in general, given a $p$-harmonic map $F:M\to N$ and a convex function $H:N\to\mathbb{R}$, the composition $H\circ F$ is not $p$-subharmonic. By assuming some rotational symmetry on manifolds and functions, we reduce the…

It is established that if a harmonic function $u$ on the unit disk $\mathbb D$ in $\mathbb C$ has angular limits on a measurable set $E$ of the unit circle $\partial\mathbb D$, then its conjugate harmonic function $v$ in $\mathbb D$ also…

We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…

A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…

We consider the inhomogeneous Dirichlet problem on product domains. The main result is the asymptotic expansion of the solution in terms of increasing smoothness up to the boundary. In particular, we show the exact nature of the…

In this manuscript we study rotationally $p$-harmonic maps between spheres. We prove that for $p\in\mathbb{N}$ given, there exist infinitely many $p$-harmonic self-maps of $\mathbb{S}^m$ for each $m\in\mathbb{N}$ with $p<m< 2+p+2\sqrt{p}$.…

A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…

This is an essay on potential theory for geometric plurisubharmonic functions. It begins with a given closed subset G of the Grassmann bundle $G(p,TX)$ of tangent $p$-planes to a riemannian manifold $X$. This determines a nonlinear partial…

We obtain rigorous results concerning the evaluation of integrals on the two sphere using complex methods. It is shown that for regular as well as singular functions which admit poles, the integral can be reduced to the calculation of…

We derive local and global monotonic quantities associated to $p$-harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relating the mass of asymptotically flat $3$-manifolds, the…

Let $m,n\geq 1$ are integers and $D$ be a domain in the $$ $\mathbb C^n$ or in the $m$-dimensional real space $\mathbb R^m$. We build positive subharmonic functions on $D$ vanishing on the boundary $\partial D$ of $D$. We use such (test)…

In this paper we develop the Perron method for solving the Dirichlet problem for the analog of the p-Laplacian, i.e. for p-harmonic functions, with Mazurkiewicz boundary values. The setting considered here is that of metric spaces, where…

In this paper, we extend some recent results of Guedj-Lu-Zeriahi about psh envelopes of bounded functions on bounded domains in $\mathbb{C}^n$. We also present a result on the regularity of psh envelopes.

We prove Liouville type theorems for $p$-harmonic functions on exterior domains of the $d$-dimensional Euclidean space, where $1<p<\infty$ and $d\geq 2$. We show that every positive $p$-harmonic function satisfying zero Dirichlet, Neumann…

We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.

1.An expression for the smoothed counting function in terms of the fractional derivatives of the delta-function is presented. 2. The Neumann-Dirichlet (ND) boundary problem is introduced via some elementary examples based on a functorial…

Let $p$ be a real number greater than one and let $G$ be a finitely generated, infinite group. In this paper we introduce the $p$-harmonic boundary of $G$. We then characterize the vanishing of the first reduced $\ell^p$-cohomology of $G$…

We present a nonvariational setting for the Neumann problem for harmonic functions that are H\"{o}lder continuous and that may have infinite Dirichlet integral. Then we introduce a space of distributions on the boundary (a space of first…